Hey! :o
I have the following in my notes:
$$u_t+A(x,t,u)u_x=b(x,t,u) \ \ \ \ \ \ \ \ \ \ (1)$$
$$u=(u_1, \dots, u_n), b=(b_1, \dots, b_n)$$
$$A=[a_{ij}], i,j = 1, \dots, n$$
We set the question if there are characteristic directions at the path of which the PDE system $(1)$ is reduced to an...